Real-time (RT) cardiac magnetic resonance (MR) cine imaging is clinically important for the diagnosis and evaluation of patients suffering from congestive heart failure, arrhythmias and other conditions. RT imaging is also beneficial in pediatric cases and under conditions where patients are unable to hold their breath. RT cardiac MR cine images are often corrupted by noise during acquisition and reconstruction. This happens because RT imaging typically sacrifices signal-to-noise ratio (SNR) to achieve sufficient temporal and spatial resolution.
Maintaining SNR is crucial in order to preserve clinically relevant information. Two factors contribute to noise in MR cine images: acquisition hardware and physiological sources. Image noise affects the quality and interpretation of clinically relevant data in varying degrees, depending on the parameters and type of image acquisition. A number of de-noising approaches have been established over the years to improve SNR of MR cine images. De-noising techniques generally fall into three broad categories: spatial filtering; temporal filtering; and a combination of spatial and temporal filtering.
Spatial filtering techniques make use of the spatial redundancies in the image. In other words, the low-spatial frequency domain contains most of the information. An example spatial filtering technique is Wavelet filtering, which is widely used for generic de-noising of images, including MR images, because it can preserve the edge better than the Fourier transform-based low-pass filter.
Temporal filtering techniques make use of the temporal redundancies in series of images acquired over time. Dynamic images of physiological process often show a high degree of temporal correlation. Since RT cardiac MR cine image series often span multiple heartbeats, they are quasi-periodic. Some frames in such image series show substantially similar features, which makes MR cine image series good candidates for temporal filtering.
Combinations of spatial and temporal filtering can be used to de-noise image series. A 3D Wavelet comprised of a 2D spatial Wavelet filter combined with a 1D temporal Wavelet filter has been proposed for video de-noising. Different spatial or temporal filters can be combined with each other depending on the characteristics of the image series. Spatial filters have been used as a means of removing noise from MR images. An example of a spatial filtering technique is Fourier-based low-pass filter. A major drawback of this method was that while removing noise, it also removes high-frequency signal components, thereby blurring the edges and fine structures in the MRI images.
Early Wavelet-based de-noising methods incorporate thresholds based on statistical models of the behavior of noise across different scales of Wavelet decomposition. These methods assume the noise is spatially white, and a single Wavelet threshold is applied. An example method proposed implements a threshold value T (a universal threshold) that is based on the standard deviation of noise and the number of samples (pixels). The main drawback with single-threshold method is there is a trade-off between signal loss and SNR gain. More aggressive threshold leads to high SNR gain and high degree of image blurring, and vice versa.
A number of Wavelet-based de-noising methods have been established to preferentially remove noise in MR images while preserving edges and details. Although methods based on scale space filtering are effective in preserving edges while removing noise, important signal details that have low amplitude might also be eliminated.
In parallel MRI, SNR reduces by at least the square root of acceleration factor and noise displays inhomogeneous spatial distribution. An edge detection algorithm may be used combined with a spatially adaptive thresholding algorithm to remove noise from images acquired using parallel MRI while preserving edge information. A specific threshold value is calculated for each pixel based on the noise map. This method makes use of soft-thresholding as well. The main disadvantage with using edge detection algorithms along with spatial filtering is that they increase complexity of the filtering process by applying separate thresholds for edge and non-edge regions. Also, output of edge detection algorithm might not always be reliable.
An alternative to edge detection algorithm is to make use of a threshold that is adaptive to the noise and signal content of the image. After Wavelet decomposition, the threshold for a specific sub-band is determined in accordance with the noise variance and the standard deviation of signal in that sub-band. Since the noise variance varies for different sub-bands, every sub-band has a unique threshold value. Temporal filters are effective in removing noise in MR images as well. One such temporal filtering method involves applying a Wavelet transform to the time-course (TC) of each pixel and performing Wavelet-domain de-noising independently on each such TC. As a consequence of WP transform, the Gaussian noise distribution is preserved in each of the sub-bands and correlated noise is effectively de-correlated across the different sub-bands of the WP decomposition.
Another temporal filtering technique is based on the Karhunen-Loeve Transform (KLT, a.k.a. Principal Component Analysis). It exploits the high temporal correlation present on real-time dynamic cardiac MR image series spanning multiple heartbeats. KLT uses this high temporal correlation to compress signal information into a finite set of eigenimages; the remaining eigenimages contain mostly noise. By using a suitable method to filter out these noise-only eigenimages, effective de-noising can be achieved. Alternatively, the KLT may be performed using singular value decomposition (SVD).
All of the filtering techniques discussed above either operate in the spatial domain or in the temporal domain. There are certain established methods that exploit redundancies in both spatial and temporal domains. Such methods use some combination of spatial and temporal filtering techniques and a selective Wavelet shrinkage method which exploits the geometry of the Wavelet sub-bands of each video frame by using a two-threshold criterion. Two criteria are typically used to determine the degree of filtering: an estimated level of noise corruption; and an amount of motion, i.e., degree of similarity between consecutive frames. However, the above method does not take advantages of the possible long-range temporal correlations in the image series, and may lead to suboptimal filtering.